Method and apparatus for optical strain sensing

ABSTRACT

Mechanical parameters of an object subjected to a force or condition are measured. A curved portion of a multicore optical fiber is attached to the object, and the multicore optical fiber includes a center core and plural off-center cores. A distributed, optically-based sensing technique is used to obtain information at each of multiple points along the curved portion from multiple ones of the cores of the multicore optical fiber. A curvature associated with the fiber attached to the object is determined using the information obtained from multiple ones of the cores. Strain information is obtained for the center core without having to obtain strain information for the off-center cores. Mechanical parameters are determined based on the strain information obtained for the center core and the curvature information obtained from the multiple ones of the cores.

PRIORITY APPLICATION

This is a continuation application which claims priority from U.S.patent application Ser. No. 13/081,056, filed on Apr. 6, 2011, whichclaims priority from U.S. provisional patent application Ser. No.61/322,430, filed on Apr. 9, 2010, the contents of which areincorporated herein by reference.

TECHNICAL FIELD

The technology relates to strain sensing, sensors, and applicationsthereof.

BACKGROUND

There is a need to separate strain and temperature for fiber sensing.Foil strain gauges may be used to measure the strain on a mechanicalstructure. FIG. 1 is an illustration of a foil gauge, which because ofits flower petals resemblance, is often called a foil gauge rosette.Foil strain sensors show similar cross sensitivities primarily due tothe dominance of the thermal expansion coefficient of the material undertest in most testing circumstances. On a structure where the orientationof the principal strain axis is unknown, a foil strain gauge rosette maybe used to measure strain in two or three axes and thus determine theprincipal strains. A rosette of three gauges may be created by placinggauges at 0, 45, and 90 degrees as shown in FIG. 1.

By measuring the strain components along three different axes, commonmode effects, such as those due to temperature changes in the materialunder test, can be removed from the strain measurement. A typical foilgauge rosette employs three strain gauges, each requiring threeelectrical connections for best use. This configuration can be tediousand bulky if multiple measurement points are required.

The inventors in this application realized that high resolution (alongthe length of the fiber) and high accuracy (in strain) strainmeasurements possible using modern fiber optic sensing systems meansthat curved lengths of fiber can be used to measure complex strainfields. Advantages of using curved fiber include smaller and moreflexible sensors along with easy production and installation of same.

SUMMARY

One or more mechanical parameters of a structure subjected to a force orcondition are measured using distributed, optical fiber sensingtechnology. At least a curved portion an optical fiber is attached to anobject. A distributed, optically-based, strain sensing technique is usedto determine strain information associated with multiple points alongthe curved portion of the fiber. The determined strain information isprocessed to generate one or more representations of one or more of thefollowing: an expansion of the object, a thermal gradient associatedwith the object, or a stress-induced strain at multiple locations on theobject corresponding to ones of the multiple points. An output isgenerated corresponding to the representation.

In non-limiting example embodiments, the optical fiber includes multiplealternating arcs and/or one or more fiber loops.

Examples of the force or condition include one or more of stress, load,temperature, temperature gradient, or higher order strain terms. Oneadvantage of this technology is that when the object is subjected to astress and to a temperature gradient, the processing can distinguishbetween temperature-induced strain and stress-induced strain.

In one non-limiting example embodiment, the distributed,optically-based, strain sensing technique is based on Rayleigh scatterin at least the curved portion of the fiber. Optical frequency domainreflectometry (OFDR) may be used, for example, to implement thistechnique. In an alternative non-limiting example embodiment, thedistributed, optically-based, strain sensing technique is based on Bragggratings positioned along at least the curved portion of the fiber.

In an example implementation, the processing is based on a relationshipbetween a change in phase in transmitted and reflected light through thecurved portion of the fiber and a change in length in the curved portionof the fiber. The processing includes taking a Fourier transform of thedetermined strain information to generate the one or morerepresentations. The Fourier transform produces a first order termcorresponding to a derivative of the change in phase that is associatedwith the expansion of the object, a first harmonic term that is ageometric function of an angle of the curved fiber portion that isassociated with the thermal gradient associated with the object, and asecond harmonic term that is a geometric function of twice an angle ofthe curved fiber portion that is associated with the stress-inducedstrain at multiple locations on the object corresponding to ones of themultiple points along the curved portion of the fiber. The Fouriertransform may also produce higher order terms higher than the secondharmonic term.

To function as a rosette, the multiple points along the curved portionof the fiber may include at least three points spaced along the curvedportion such that a first one of the points is oriented at zero degrees,a second one of the points is oriented 90 degrees from the first point,and a third one of the points is oriented between the first and secondpoints.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an illustration of a foil strain gauge rosette;

FIG. 2 is a strain rosette using discrete Bragg gratings;

FIG. 3 shows a curving optical fiber with oscillating quarter arcs;

FIG. 4 shows an example fiber loop strain sensor;

FIG. 5 shows the angle and radius of a circle loop;

FIGS. 6A and 6B show tension and compression on a test plate;

FIGS. 7A-7C show effects of applying a uni-axial load to a test platewith a fiber loop bonded to its surface;

FIGS. 8A-8D illustrate effects of thermal changes applied to a testplate;

FIGS. 9A-9E illustrates various strain states on a test plate that leadto different harmonics in a strain signal measured around a fiber looprosette;

FIG. 10 illustrates periodic strain measured around the circumference ofthe fiber loop;

FIG. 11A is a function block diagram of an OFDR system for measuringstrain of a test plate using multiple fiber loops bonded to the testplate;

FIG. 11B is a diagram of an example, non-limiting OFDR system;

FIG. 12 is a flowchart diagram illustrating example, non-limitingprocedures for calculating one or more strain related parameters usingthe example system shown in FIGS. 11A and 11B;

FIG. 13 is a diagram of two concentric fiber loops bonded onto a testsample;

FIG. 14 is a graph illustrating optical displacement as a function ofdistance along the sensing fiber for the test sample in FIG. 13;

FIG. 15 is a closer view from FIG. 14 of the optical distance changealong the length of fiber in the one inch diameter loop;

FIG. 16 is a graph illustrating strain along the fiber on the innerconcentric fiber loop for the test sample in FIG. 13;

FIG. 17 is a graph illustrating strain along the fiber on the innerconcentric fiber loop with the sample straight in a load frame (solid)and angled 12 degrees in the load frame (dashed);

FIGS. 18A and 18B shows gray scale-coded strain plotted around loop forthe sample held a) vertically in the load frame and b) tilted 12 degreesin the load frame;

FIG. 19 is a plot of the Fourier transform of the strain around a singleone inch fiber loop for different loads;

FIG. 20 is a graph of strain as a function of distance along thecircumference of the one inch diameter loop for two temperature gradientconfigurations;

FIG. 21 is a graph of a Fourier analysis of two thermal gradients, withone induced horizontally and the other induced vertically; and

FIGS. 22A and 22B are gray scale-coded strain plotted around the loopfor two induced temperature gradients.

DETAILED DESCRIPTION

The following description sets forth specific details, such asparticular embodiments for purposes of explanation and not limitation.But it will be appreciated by one skilled in the art that otherembodiments may be employed apart from these specific details. In someinstances, detailed descriptions of well known methods, interfaces,circuits, and devices are omitted so as not obscure the description withunnecessary detail. Individual blocks are shown in the figurescorresponding to various nodes. Those skilled in the art will appreciatethat the functions of those blocks may be implemented using individualhardware circuits, using software programs and data in conjunction witha suitably programmed digital microprocessor or general purposecomputer, and/or using applications specific integrated circuitry(ASIC), and/or using one or more digital signal processors (DSPs).Software program instructions and data may be stored on acomputer-readable storage medium, and when the instructions are executedby a computer or other suitable processor control, the computer orprocessor performs the functions.

Thus, for example, it will be appreciated by those skilled in the artthat diagrams herein can represent conceptual views of illustrativecircuitry or other functional units. Similarly, it will be appreciatedthat any flow charts, state transition diagrams, pseudocode, and thelike represent various processes which may be substantially representedin computer-readable medium and so executed by a computer or processor,whether or not such computer or processor is explicitly shown.

The functions of the various illustrated elements may be providedthrough the use of hardware such as circuit hardware and/or hardwarecapable of executing software in the form of coded instructions storedon computer-readable medium. Thus, such functions and illustratedfunctional blocks are to be understood as being eitherhardware-implemented and/or computer-implemented, and thusmachine-implemented.

In terms of hardware implementation, the functional blocks may includeor encompass, without limitation, a digital signal processor (DSP)hardware, a reduced instruction set processor, hardware (e.g., digitalor analog) circuitry including but not limited to application specificintegrated circuit(s) (ASIC) and/or field programmable gate array(s)(FPGA(s)), and (where appropriate) state machines capable of performingsuch functions.

In terms of computer implementation, a computer is generally understoodto comprise one or more processors or one or more controllers, and theterms computer, processor, and controller may be employedinterchangeably. When provided by a computer, processor, or controller,the functions may be provided by a single dedicated computer orprocessor or controller, by a single shared computer or processor orcontroller, or by a plurality of individual computers or processors orcontrollers, some of which may be shared or distributed. Moreover, theterm “processor” or “controller” also refers to other hardware capableof performing such functions and/or executing software, such as theexample hardware recited above.

Optical fiber rosette structures may be designed by substituting a fiberwith a Bragg grating for each of the strain gauges above. The design ofsuch a structure tends to be driven by the length of the Bragg gratingsand the perceived need to have the entire grating parallel to the senseddirection of strain. An example of such a rosette constructed using alength of optical fiber with three Bragg gratings is shown in FIG. 2.But such a rosette does not have the full advantages afforded bydistributed fiber strain sensing. Examples of distributed fiber strainsensing are described in commonly-assigned U.S. Pat. Nos. 5,798,521;6,545,760; 6,566,648; 7,440,087; and 7,772,541, all of which areincorporated herein by reference.

A fiber rosette that can be used to take full advantage of distributedfiber strain sensing may be formed by curving (“wiggling”) the fiber ina series of periodic, circular arcs. The arcs preferably cover 90degrees to get a measure of the strain components covered by a typicalrosette. A distributed measurement of the strain along the fiber sincethe sensed strain is constantly oscillating. This periodic nature of thestrain decomposition means that Fourier transforms can be used in theanalysis of the measured strain in the fiber and to convert a onedimensional oscillatory strain into multiple strain-related parametersincluding: an isotropic expansion and two orthogonal strain fields.Distributed strain measurement may be achieved by using a Rayleighscatter based strain measurement or a Bragg grating based measurementwith a phase derivative calculation to find the strain continuouslyalong the grating as described in the patents incorporated by referenceabove. In summary, commercially available OFDR systems can measurereflected signals below −130 dB with tens of microns of spatialresolution. As such, they offer a sensitive and accurate measurement ofthe Rayleigh scatter reflected from standard optical fiber. The spatialpattern of this scatter is formed in the fiber when it is manufacturedand is a random, but repeatable, pattern that is unique in each fiber.This scatter pattern forms the “sensor” used for Rayleigh scatter-based,OFDR distributed sensing. When the fiber is strained, this scatterpattern is stretched which leads to a shift in the frequency spectrumreflected from the stretched section of fiber just as the reflectedfrequency of a Bragg grating shifts when it is stretched or strained.The reflected spectrum of a given segment of fiber as measured usingOFDR can be found by windowing the complex data at the desired locationand performing an inverse Fourier transform.

FIG. 3 shows an example of a curved fiber with quarter arcs thatcorrespond to six rosette strain sensors. This quarter-arc curved fiberis only 11% longer than a straight fiber. A half-arc curved fiber wouldbe 57% longer, but would provide for strain vectors parallel andperpendicular to the layout direction. If the fiber has a high numericalaperture, a small bend radius may be used, e.g., 3 mm, to create arosette every 5 mm long the fiber. In one non-limiting example, curvedfiber is approximately 80 microns in diameter and mounted in polyamidetape or other adhesive that for bonding the fiber the surface of theobject to be tested. Such a curved fiber could also be embedded/formedwithin the object to be tested. The terminology “attached to the object”encompasses any means or way that allows the curved fiber to move withmovement of the object.

A fiber rosette can also be formed from a full circular loop of fiber.FIG. 4 shows an example of a fiber loop strain sensor. While a full loopsensor is more expensive in terms of meters of fiber per length ofcoverage, it allows for a simplified analysis of strain. Being able todo a closed line integral:o∫ g(l)·d lwhere g is a function along the length of the fiber, and dl is thedifferential vector in the direction of the fiber at that point. Inpractice, g may be a scalar or a vector. Later, a specific case is usedwhere g is the measured strain, and in the case of a circular fiberloop, dl is the sine and cosine of the length, leading to an expressionin the form of a Fourier transform. Because closed line integrals occurso frequently in math and physics, many additional uses and applicationsare envisioned.

As explained above, a discrete Fourier transform of the strain ordeformation around the loop may be used to separate individualstrain-related parameters in a fiber loop configuration. In this case,the x and y coordinates are mapped on the surface space to the real andimaginary components of a complex number. This provides a way ofhandling the two dimensional vector in a compact notational form as wellas takes advantage of a large body of mathematics around complexnumbers. The first term of the integral is the average, total expansionof the material in the optical loop. The next term is the gradient ofthis expansion field in the complex plane (x is real and y is imaginary)across the fiber loop. The third term (second harmonic term) containsinformation about the x and y strain levels, and when combined with thezero'th frequency term, gives the strain levels in the x and ydirections. The higher order terms may also have useful physicalinterpretations and uses.

To help illustrate some of the terminology used in this application,consider a plate as an object to be tested. The definition of stress isforce per unit area. Stress that lengthens an object is known astension, and stress that shortens an object is known as compression.Strain is the ratio of length change to total length caused by theapplied stress. FIG. 6A illustrates an object being pulled from bothends along a horizontal axis. This force lengthens the object, puttingit under tension and causing positive strain. FIG. 6B illustrates anobject under compression along the horizontal axis leading to negativestrain.

FIGS. 7A-7C illustrate the effects of applying a uniaxial load to a testplate with an optical fiber loop bonded to the surface. FIGS. 7A showsthat uniaxial loading along the horizontal axis causes tension, orpositive strain, on the locations of the loop whose tangents areparallel to the horizontal axis. The Poisson effect causes compressionin portions in the vertical axis. This negative strain is measured inthe loop at locations where the tangent is perpendicular to thehorizontal axis. FIGS. 7B illustrates a uniaxial load in the verticalaxis. In this case, there is tension, or positive strain, at points inthe loop where the tangent is parallel to the vertical axis, andcompression, or negative strain occurs at points in the loop where thetangent is perpendicular to the vertical axis. FIGS. 7C illustrates auniaxial load at an arbitrary angle. Again, tension occurs along theaxis of the applied load, and compression occurs perpendicular to thisaxis. The direction of the strain in these figures is the direction ofthe principle strain.

FIGS. 8A-8D illustrate the effects of thermal changes applied to a testplate. FIG. 8A shows the plate in a nominal state. FIG. 8B shows theeffect of heating the plate uniformly. The plate expands according tothe material's coefficient of thermal expansion. The fiber loopexperiences tension all around the loop and positive strain is measuredall along the fiber loop bonded to the surface. FIG. 8C illustrates theeffect of cooling the plate uniformly. In this case, the plate iscompressed and negative strains are measured around the entire fiberloop. FIG. 8D illustrates the strains experienced when a thermalgradient is applied to the test plate. On the left, the plate is heatedand the material expands, causing tension or positive strain along theleft side of the loop. On the right, the plate is cooled and thematerial shrinks, leading to compression or negative strain on the rightside of the loop. The strain changes in a smooth, sinusoidal patternaround the loop between the points of maximum compression and tension,creating a single sinusoid with a period equal to the length of theloop's circumference.

FIGS. 9A-9E illustrate various strain states on a sample plate that leadto different harmonics in the strain signal measured around a fiber looprosette. Outward pointing arrows represent expansion, tension, orpositive strain. Inward pointing arrows represent compression ornegative strain. FIG. 9A shows that uniform compression or expansion ofthe plate can be caused by uniform cooling or heating and leads to aconstant change in the strain measured around the loop when compared tothe strain in a nominal state. This is a D.C. signal, or the 0^(th)harmonic. FIG. 9B shows a thermal gradient applied to the loop resultingin a single sinusoidal strain signal, or 1^(st) order harmonic, asillustrated in the FIG. 8D. The loop is under tension where the sampleis heated (left side in FIG. 8D) and under compression where the sampleis cooled (right side in FIG. 8D). FIG. 9C illustrates a 2^(nd) orderharmonic strain signal. This can be caused by uniform, uniaxial loadingof a test sample as illustrated in FIGS. 7A-7C. FIGS. 9D and 9Eillustrate 3^(rd) order and 4^(th) order harmonics, respectively.

As described in the patents incorporated by reference above, when theoptically-sensed strain data is processed in a continuous fashion, thetotal accumulated phase change along a length of fiber can be measuredwith high accuracy. The accumulated phase change as a function ofdistance represents the total change in the time of flight of light inthe fiber or the effective change in fiber length. In this example case,the integral of the strain is measured with high accuracy. Thederivative of this total change in the time of flight of light in thefiber or the effective change in fiber length is proportional to thestrain or temperature change in the fiber. The relationship between thechange in effective fiber length and phase change is expressed:

$\begin{matrix}{{\Delta\varphi} = {2\pi\; n\;\frac{2\Delta\; L_{eff}}{\lambda}}} & (1)\end{matrix}$

where Δφ is the change in optical phase, n is the group index of theoptical fiber, ΔL_(eff) is the effective change in length, and λ is theoptical wavelength. The effective length includes effects due to changesin the index of refraction and can be expressed as follows:

$\begin{matrix}{{\Delta\; L_{eff}} = {{\Delta\; L} + {L\;\frac{\Delta\; n}{n}}}} & (2)\end{matrix}$

Using an approximate group index of 1.5 and a wavelength of 1500 nm, aneffective change in fiber length of 250 nm causes a π phase change. Theeffective change in length is related to the strain applied to the fiberby a proportionality constant related to the strain-optic coefficient kas shown in Eq. 3:

$\begin{matrix}{\frac{\Delta\;\varphi}{\varphi} = {\frac{\Delta\; L_{eff}}{L} = {k\; ɛ}}} & (3)\end{matrix}$Typical material properties for germanium doped silica yield a value ofk=0.787.

As mentioned above, Fourier analysis can be used to analyze the straindata and glean information about the measured strain field. Let thetotal length change in the fiber loop be given by Δφ(z) where z is thedistance along the fiber core (ø is chosen for the function because achange in optical phase is measured in this example). The averageexpansion over the fiber-encircled area on the object to be tested isthen proportional to the total length change of the fiber loop attachedto that object or:ε₀ =k[Δφ(c)−Δφ(0)]  (4)Here, ε₀ is the expansion of the material under test, k is aproportionality constant that involves the strain-optic coefficient ofthe fiber, C is the circumference of the loop, and Δφ(z) is the opticalphase change from a zero level measurement of the object under testtaken earlier.

If the object under test changes in such a way that the loop isstretched on one side and compressed by another, then this effectappears as a first harmonic and is illustrated in FIG. 8D. This is thecase, for example, if a thermal gradient is applied to the sample, thisterm can be expressed as:ε₁(z)=ε_(x,1) cos(θ)+iε _(y,1) sin(θ)   (5)Where θ=z/r is the angle around the circle shown in FIG. 5 calculatedfrom z, the distance along the fiber core and r, the radius of thecircle as shown in FIG. 5. ε_(x) and ε_(y) are the strains in theorthogonal directions, x and y, in the complex plane.

If a uniaxial strain is applied to the surface of the object to whichthe fiber loop is attached, then a second harmonic term is generated,i.e., two periods of a sinusoidal strain pattern around the loop. Anillustration of the way in which a uniform strain field generates asecond harmonic in the loop is described in conjunction with FIG. 10.FIG. 10 shows the periodic strain field that would be measured movingaround the circumference of the fiber loop. This strain pattern can beexpressed as:ε₂(z)=ε_(x,2) cos(2θ)+is _(y,2) sin(2θ)   (6)Note that as the direction of the strain field rotates, the phase of thesecond harmonic term will shift. This phase shift in radians directlytranslates to the rotational shift in radians (with a factor of twodifference).

Given the relationship between the derivative of the phase change from areference state and the applied strain, the various Fourier elements ofthe strain field may be expressed by:

$\begin{matrix}{{ɛ_{m}(z)} = {{k\frac{2\pi}{C}{\int_{0}^{C}{\left\lbrack {\Delta\;{\phi(z)}} \right\rbrack^{\prime}{\mathbb{e}}^{{\mathbb{i}}\;\frac{2\pi\; m}{C}z}{\mathbb{d}z}}}} = {k{\int_{0}^{2\pi}{\left\lbrack {\Delta\;{\phi(\theta)}} \right\rbrack^{\prime}{\mathbb{e}}^{{\mathbb{i}}\; m\;\theta}{\mathbb{d}\theta}}}}}} & (7)\end{matrix}$where k is the proportionality constant related to the strain-opticcoefficient. The term ε₁ can be interpreted as the gradient of theexpansion field from a non-uniform thermal field. Because a real andimaginary part results from the calculation, the direction as well asthe magnitude of the gradient can be resolved. The term ε₂ gives thecomponents of the uniform strain over the loop, and when combined withε₀, gives the total strain field.

A shape sensing fiber may be used to deduce the location and radius ofsuch a loop as described above. A detailed description of a shapesensing fiber is described in “Optical Position and/or Shape Sensing,”U.S. application Ser. No. 12/874,901, incorporated herein by reference.Even an 80 micron diameter fiber can support 4 cores by spacing theoff-center cores 40 microns from the center. Such a multi-core fiber isnot expensive, and can be used to map out the geometric layout of thecurved fiber in both loop-curve and arc-curve configurations.

As shape systems improve, a 125 micron shape sensing fiber bonded tocomplex structures may be used to map out the shape of the attachedfiber. If a numerical model of the mechanical part under test isdetermined, then the set of locations along the fiber may be matched upto the mechanical model, and the individual points of the fiber strainmeasurement (along with the axis over which the strain is measured) maybe mapped directly to the mechanical structure's surface.

FIG. 11A is a non-limiting example block diagram of an optical frequencydomain reflectometry (OFDR) measurement system for measuring strain infiber loop rosettes on a test sample. OFDR enables measurements of theamplitude and phase of the light backscattered along a fiber with highsensitivity and high spatial resolution. This measurement, in turn,makes it possible to detect the shift in the reflected spectrum of thescattered light as a function of distance down the fiber due to appliedstrain or temperature changes. The OFDR measurement system is connectedto a computer or controller for system control and data processing. TheOFDR measurement system is optically connected to a device or objectunder test via an optical fiber that includes two fiber loops (in thisexample) attached to the object. It should be appreciated that thetechnology may be used with a fiber having just one or multiple curvedportions (arcs) being attached to the object. The OFDR system measuresthe light reflected from the attached fiber and the computer systemdetermines multiple strain related parameters based on the mathematicsdescribed above. The technology in this application, though well-suitedfor OFDR-based measurement, may be used with other fiber-optic-basedmeasurement techniques such as but not limited to path matching whitelight interferometer, ultra-fast laser pulse interferometry, highresolution Brillion scatter sensing, and wave division multiplexing ofBragg gratings.

Ultimately, the computer generates an output associated with orcorresponding to one of more of multiple strain-related parametersincluding but not limited to an expansion of the object, a thermalgradient associated with the object, and/or a stress-induced strain atmultiple locations on the object corresponding to ones of the multiplepoints along the curved portion of the fiber. The output could be anyuseful information useable by a human or a machine including a display,an alarm, a file, or a stream of strain and/or temperature data comingover a communication link.

FIG. 11B shows schematically a non-limiting example of an opticalnetwork that can be used for OFDR measurements in FIG. 11A. OtherOFDR-based networks could be used. Light from a tunable laser (TLS) issplit at coupler C1 between two interferometers. Light going to theupper interferometer is split at coupler C4 between two fibers with adelay difference, τ, connected to Faraday rotator mirrors (FRMs) toensure polarization variations do not disturb the interference signal.The interference fringes caused by recombining the light from these twopaths at coupler C4 are detected and used to trigger data acquisition sothat data is taken in equal increments of optical frequency as the lasertunes. The lower interferometer splits the incoming laser light betweena reference path and a measurement path at coupler C2. The light in themeasurement path travels to the fiber which is attached to the objectunder test and reflected light returns through an optical circulator.The reference and measurement light are recombined at coupler C3. Thepolarization controller (PC) in the reference path is used to ensurethat light in this path is aligned with the axis of the polarizationbeam splitter such that it is split evenly between the two opticaldetectors labeled S and P. This polarization diverse detection schemeenables a consistent measure of the reflected light regardless of itspolarization state. The data acquired at the optical detectors S and Pas the laser tunes through a given wavelength range is thenFourier-transformed. The Fourier-transformed S and P data are combinedto yield the amplitude and phase of the reflected light as a function ofdistance.

FIG. 12 is a flowchart diagram of non-limiting example procedures thatmay be performed using the OFDR measurement system of FIGS. 11A and 11B.After one or more optical fiber arc or loop curves is attached to theobject, the OFDR measurement system measures a state A of the fibercurve(s) attached (step S1), where this measurement of state A containsthe phase relationships and amplitudes of each of the scatter points inthe optical fiber at the particular time of the measurement using adistributed, optically-based, strain sensing technique in at least thecurved portion of the fiber and stores state A (step S2). Thedistributed, optically-based, strain sensing technique may be based forexample on Rayleigh scatter and/or using multiple Bragg gratings in atleast the curved portion(s) of the fiber. The object is exposed to someforce or condition, e.g., a load, temperature, etc., (step S3), and theOFDR measurement system measures a state B of the fiber curve(s)attached (step S4). The computer compares (e.g., differentiates orcorrelates) state A to state B and determines a distributed strainaround the curve (step S5). One or more desired strain parameters arecalculated from that distributed strain including but not limited to anexpansion of the object, a thermal gradient associated with the object,a stress-induced strain a multiple locations/points on the object, orhigher order strain terms such as those illustrated in FIGS. 9D and 9E(step S5). The calculations include taking a frequency transform of thedistributed strain information.

In one example operation, the OFDR system sweeps a tunable laser over awavelength range, and recording the interference effects on the threedetectors shown in FIG. 11B. The signal on the trigger detector is usedas an accurate measure of the laser tuning, and this measurement is usedto convert the data acquired on the S and P detectors into a signal thatis precisely linear in laser frequency (this is described in detail inU.S. Pat. Nos. 5,798,521 and 6,566,648 incorporated herein byreference). A Fourier transform is then taken of the each of these S andP signals, and the result of this transform then represents the complex(phase and amplitude) scatter at each point along the fiber. Initially,a measurement is performed on the fiber in a “zero” or reference state,and this data is stored. Later, another measurement is made in anunknown state, and the phase change along the length of the fiber ismeasured to produce a measurement of the total fiber length change ateach point along the fiber. A detailed description of this process is in“Optical Position and/or Shape Sensing,” U.S. application Ser. No.12/874,901, incorporated herein by reference. From this measurement ofthe total length change in the fiber, a strain can be calculated simplyby calculating the rate of change of the length as a function of theoverall length.

A non-limiting, example test from single core fiber with multiple loopsis now described. As a test example, a 125 micron glass diameterpolyimide coated high numerical aperture single mode optical fiber wasbonded in two concentric circles on a 10×6 inch aluminum plate 0.25inches thick. The interior circle was one inch in diameter, and theexterior circle was two inches in diameter. Two smaller loops werebonded only at the base to serve as unconstrained temperature sensors.Various loads were applied to the sample using a load frame. Anextensometer with a one inch gage length was attached to the sample toprovide a reference measurement. FIG. 13 illustrates the two loop fiberpath on the test plate. The smaller one inch loop was included withinthe larger two inch loop. The bolded arrows indicate the direction ofthe loading for when the plate was held straight.

The plate was subjected to increasing load levels, and the Rayleighscatter signature was used to measure the phase change along the core ofthe optical fiber as described in U.S. application Ser. No. 12/874,901,entitled Optical Position and/or Shape Sensing, which is incorporatedherein by reference.

In order to accurately track the accumulated phase change along thelength of the fiber, the phase is preferably measured with a spatialresolution high enough such that the phase does not change by more than±π within the spatial resolution. Otherwise, a phase change of π+δ isindistinguishable from a change of δ, and errors are introduced in thephase measurements. For the measurements taken in the test, the scanrange was 5 nm yielding a spatial resolution of 160 μm. Using the valuefor k mentioned above, a π phase change in a 160 μm step represents anapplied strain of about ±2,000 με. In order to measure strains largerthan this, a longer scan range can be used to achieve a higher spatialresolution. The phase change along the fiber, converted to displacementin nanometers, is shown in FIG. 14. FIG. 14 graphs optical displacementas a function of distance along the sensing fiber. Displacements forvarious loads 205, 567, 765, 100, 1300, and 1350 lbf are shown. Fourmeasurements were taken at the load of 1350 lbf. FIG. 15 shows a closerview of the optical distance change along the length of fiber in the oneinch diameter loop. The displacements for the loads 205, 567, 765, 100,1300, and 1350 lbf are shown. Four measurements were taken at the load1350 lbf.

If a length of fiber is selected to wrap around the circumference of theone inch diameter circle and the strain around it is calculated, theperiodic strain fields shown below in FIG. 16 are produced. The strainsfor loads 205, 567, 765, 100, 1300, and 1350 lbf are shown. For the fourmeasurements at the load 1350 lbf, the maximum variation across the fourmeasurements at any given location is 6 με. The average standarddeviation over all locations at this load level is 1.26 με.

Table 1 shows a comparison of the strain data as measured with theextensometer with the maximum strain measured in the fiber loop. A point64 mm into the loop at the maximum strain location as shown in FIG. 16was used for the fiber data. This comparison shows that the fibermeasurements varied from the extensometer results only by a maximum of 7με and an average of 3 με.

TABLE 1 Load Extensometer (lbf) Fiber (με) (με )  205 33 26  567 85 81 765 109 109 1000 147 145 1300 192 189 1350 203 200

FIG. 17 shows the strain along the fiber on the one inch loop with thesample straight in the load frame (solid) and angled 12 degrees in theload frame (dashed). In this data, the strain data from in the angledstate is shifted in phase with respect to the straight data. Thedirection of the applied load can be determined from the phase shift inthe data. Here it is useful to show the circle with the strain levelsshown on a gray scale. FIGS. 18A and 18B show two such plots: FIG. 18Awith the plate held straight, and FIG. 18B with the plate is tilted bytwelve degrees to illustrate the ability of the loop to discriminate thedirection of the applied uniaxial strain.

A Fourier transform of the distributed strain data reveals that only thefundamental 0^(th) (average value) term and 2^(nd) harmonic havesubstantial signal levels present. The amplitude of the 2^(nd) harmonicis a measure of the uniaxial stress present. The phase of the 2^(nd)harmonic term is an indication of the direction of the applied stress.FIG. 19 graphs the Fourier transform of the strain around a single oneinch fiber loop for 205, 567, 765, 100, 1300, and 1350 lbf loads areshown. Four measurements were taken at 1350 lbf. In the case of thestraight pull data, where the applied force was in the direction of thelong length edge of the sample, the phase was 165.5 degrees. The angleddata, where the sample was pulled in a direction different from the longlength edge of the sample, had a phase of 193.8 degrees. The differencein the pull direction was (193.8−165.5)/2=14 degrees, which isreasonably close to the actual tilt of the plate, as measured with aprotractor, i.e., 12 degrees.

A homogeneous rise in the temperature causes a uniform expansion of thefiber loop and only creates a Fourier component at the 0^(th) harmonic.A temperature gradient, however, produces a signal at the firstharmonic. Although obtaining a uniform thermal gradient may be difficultin some circumstances, relatively non-uniform gradients can usually beused with success. The strain fields around the loop for a vertical andhorizontally induced strain field is shown in FIG. 20 (strain as afunction of distance along the circumference of the one inch diameterloop for two temperature gradient configurations), and a Fourieranalysis is shown in FIG. 21 (Fourier analysis of two thermal gradientswith one induced horizontally and the other induced vertically).

Again, the phase of the first harmonic is used to indicate the directionof thermal gradient. The phase of the vertical thermal gradient is −15degrees, and the phase of the horizontal thermal gradient is 80 degrees,which puts the angular difference between the two at 95 degrees, whichis about as close as could be expected with the crude apparatus used toinduce the gradient. FIGS. 22A and 22B show the thermally induced strainfields around the loop showing the directional nature of themeasurement.

One can take similar data as shown above with closely-spaced fiber Bragggratings (FBGs) using a wave division multiplex (WDM) distributedsensing technique. But there may be some limit in this case on the sizeof the fiber loop. In the case of the one inch loop used above, oneexample might use eight FBGs spaced at 1 cm intervals to attain adesired resolution. Even smaller fiber loops, e.g., one cm diameter, maybe used to produce similar results. The loop size is mainly limited bythe material properties of the fiber. For example, an 80 μm outerdiameter fiber could be used to form smaller loops. For small loopsizes, placing enough FBGs in the fiber loop is less feasible, and ahigh-resolution continuous sensing technique is likely preferable.

Fiber optic sensors are advantageous because they are light, immune toelectromagnetic interference, and relatively easily multiplexed. Thehighly distributed nature of OFDR sensing technique described above canreplace traditional electrical strain gages, including rosette straingages, in applications where large numbers of strain measurements arerequired. By placing an optical fiber in a loop, strain is projectedalong the fiber at a continuum of angles traversing the loop.Distributed OFDR techniques can measure the strain with high resolution(currently better than every millimeter), and thus provide numerousindependent strain measurements around the loop. For example, a 1 cmdiameter loop may include about 30 one millimeter strain sensingsections. These measurements around the loop can be used to calculateseveral parameters with good accuracy including resolving the straininto uniform expansion (such as a rise in overall temperature wouldcause), strain in the horizontal direction (0 degrees), and strain inthe vertical direction (90 degrees). In addition, vertical andhorizontal gradients can also be acquired, as well as higher orderterms. distributed nature of OFDR sensing technique described above maybe used for example in the testing of structures designed to carry heavyloads such as submarines or ships as well as structures designed tocarry heavy loads and to simultaneously be light weight, such asaircraft or automobiles. Finally, the highly distributed nature of themeasurement and the ability to make multiple small loops that do notinterference with the structure (only a single fiber lead) means thatthe technique can be used in biomechanics and other mechanicalstructures that are small and complex.

The technology uses a curved fiber attached to an object to measurestrain components in more than one direction. Other strain measurementtechniques, including traditional electrical strain gages and otherfiber optic methods, require straight sensing areas over which thestrain is uniform. Eliminating this straight section requirement, thedisclosed technology simplifies the application and installation of thesensor and makes the sensor more compatible with higher degrees ofmultiplexing since loops or curves are easily cascaded. The techniquedescribed allows the use of unaltered, off-the-shelf fiber and providesan inexpensive, single connection strain rosette. Multiple rosettes maybe formed in a single fiber placed as desired on a structure to providea more detailed picture of the stresses.

Although various embodiments have been shown and described in detail,the claims are not limited to any particular embodiment or example. Noneof the above description should be read as implying that any particularelement, step, range, or function is essential such that it must beincluded in the claims scope. The scope of patented subject matter isdefined only by the claims. The extent of legal protection is defined bythe words recited in the allowed claims and their equivalents. Allstructural and functional equivalents to the elements of theabove-described preferred embodiment that are known to those of ordinaryskill in the art are expressly incorporated herein by reference and areintended to be encompassed by the present claims. Moreover, it is notnecessary for a device or method to address each and every problemsought to be solved by the technology described, for it to beencompassed by the present claims. No claim is intended to invokeparagraph 6 of 35 USC §112 unless the words “means for” or “step for”are used. Furthermore, no embodiment, feature, component, or step inthis specification is intended to be dedicated to the public regardlessof whether the embodiment, feature, component, or step is recited in theclaims.

The invention claimed is:
 1. A method for measuring one or moremechanical parameters of an object subjected to a force or condition,where at least a curved portion of a multicore optical fiber is attachedto the object, the multicore optical fiber having a center core andplural off-center cores, the method comprising: using a distributed,optically-based sensing technique to obtain information at each ofmultiple points along the curved portion from multiple ones of the coresof the multicore optical fiber; determining a curvature associated withthe multicore optical fiber that is attached to the object using theinformation obtained from multiple ones of the cores of the multicoreoptical fiber; using a distributed, optically-based, strain sensingtechnique to obtain strain information for the center core withouthaving to obtain strain information for the off-center cores;determining the one or more mechanical parameters of the object based onthe strain information obtained for the center core and the curvatureinformation obtained from the multiple ones of the cores; and generatingan output corresponding to a representation of the determined one ormore mechanical parameters.
 2. The method in claim 1, wherein thecurvature is determined at a first time, the method further comprisingdetermining the one or more mechanical parameters at multiple othertimes based on the curvature determined at the first time and straininformation obtained for the multiple other times.
 3. The method inclaim 1, further comprising determining a location and a radiusassociated with the multicore optical fiber that is attached to theobject based on the determined curvature.
 4. The method in claim 1,further comprising determining a shape associated with the multicoreoptical fiber that is attached to the object based on the determinedcurvature.
 5. The method in claim 1, wherein the curved portion includesone or more arcs associated with the multicore optical fiber that isattached to the object, and wherein the shape includes one or moreconfigurations of the one or more arcs.
 6. The method in claim 1,further comprising: processing the optically sensed strain data in acontinuous fashion to determine a total accumulated phase change along alength of the multicore optical fiber that is attached to the object,and using the total accumulated phase change to increase the accuracy ofthe determined one or more mechanical parameters.
 7. The method in claim6, wherein the processing is based on a relationship between a change inphase in transmitted and reflected light through the curved portion ofthe fiber and a change in length in the curved portion of the fiber, andwherein the processing includes taking a Fourier transform of thedetermined strain information to generate the one or morerepresentations.
 8. The method in claim 1, wherein the one or moremechanical parameters includes: an expansion of the object, a thermalgradient associated with the object, or a stress-induced strain atmultiple locations on the object corresponding to ones of the multiplepoints along the curved portion of the fiber.
 9. The method in claim 1,wherein the force or condition includes one or more of stress, load,temperature, temperature gradient, or higher order strain terms. 10.Apparatus for measuring one or more mechanical parameters of an objectsubjected to a force or condition, where at least a curved portion of amulticore optical fiber is attached to the object, the multicore opticalfiber having a center core and plural off-center cores, the apparatuscomprising electronic circuitry configured to: use a distributed,optically-based sensing technique to obtain information at each ofmultiple points along the curved portion from multiple ones of the coresof the multicore optical fiber; determine a curvature associated withthe multicore optical fiber that is attached to the object using theinformation obtained from multiple ones of the cores of the multicoreoptical fiber; use a distributed, optically-based, strain sensingtechnique to obtain strain information for the center core withouthaving to obtain strain information for the off-center cores; determinethe one or more mechanical parameters of the object based on the straininformation obtained for the center core and the curvature informationobtained from the multiple ones of the cores; and generate an outputcorresponding to a representation of the determined one or moremechanical parameters.
 11. The apparatus in claim 10, wherein theelectronic circuitry is configured to: determine the curvature at afirst time, and determine the one or more mechanical parameters atmultiple other times based on the curvature determined at the first timeand strain information obtained for the multiple other times.
 12. Theapparatus in claim 10, wherein the electronic circuitry is configured todetermine a location and a radius associated with the multicore opticalfiber that is attached to the object based on the determined curvature.13. The apparatus in claim 10, wherein the electronic circuitry isconfigured to determine a shape associated with the multicore opticalfiber that is attached to the object based on the determined curvature.14. The apparatus in claim 10, wherein the curved portion includes oneor more arcs associated with the multicore optical fiber that isattached to the object, and wherein the shape includes one or moreconfigurations of the one or more arcs.
 15. The apparatus in claim 10,wherein the electronic circuitry is configured to process the opticallysensed strain data in a continuous fashion to determine a totalaccumulated phase change along a length of the multicore optical fiberthat is attached to the object, and use the total accumulated phasechange to increase the accuracy of the determined one or more mechanicalparameters.
 16. The apparatus in claim 15, wherein the processing isbased on a relationship between a change in phase in transmitted andreflected light through the curved portion of the fiber and a change inlength in the curved portion of the fiber, and wherein the processingincludes taking a Fourier transform of the determined strain informationto generate the one or more representations.
 17. The apparatus in claim10, wherein the one or more mechanical parameters includes: an expansionof the object, a thermal gradient associated with the object, or astress-induced strain at multiple locations on the object correspondingto ones of the multiple points along the curved portion of the fiber.18. The apparatus in claim 10, wherein the electronic circuitry includesan optical frequency domain reflectometer.